Data-driven Spatiotemporal Modal Decomposition for Time Frequency Analysis

TL;DR

This paper introduces STIMD, a novel data-driven method for spatiotemporal modal decomposition that improves non-stationary signal analysis and prediction by leveraging intrinsic mode functions across multiple dimensions.

Contribution

STIMD extends empirical mode decomposition to multi-dimensional signals, enabling better extraction of interpretable modes and future-state prediction in complex spatiotemporal data.

Findings

STIMD outperforms SVD, ICA, and DMD in reconstruction accuracy.

STIMD provides more interpretable modes for non-stationary data.

Successful application to gravitational wave and neural data demonstrates its effectiveness.

Abstract

We propose a new solution to the blind source separation problem that factors mixed time-series signals into a sum of spatiotemporal modes, with the constraint that the temporal components are intrinsic mode functions (IMF's). The key motivation is that IMF's allow the computation of meaningful Hilbert transforms of non-stationary data, from which instantaneous time-frequency representations may be derived. Our spatiotemporal intrinsic mode decomposition (STIMD) method leverages spatial correlations to generalize the extraction of IMF's from one-dimensional signals, commonly performed using the empirical mode decomposition (EMD), to multi-dimensional signals. Further, this data-driven method enables future-state prediction. We demonstrate STIMD on several synthetic examples, comparing it to common matrix factorization techniques, namely singular value decomposition (SVD), independent component analysis (ICA), and dynamic mode decomposition (DMD). We show that STIMD outperforms these methods at reconstruction and extracting interpretable modes. Next, we apply STIMD to analyze two real-world datasets, gravitational wave data and neural recordings from the rodent hippocampus.